Symbolic vector analysis in plasma physics. H. Qin, W.M. Tang, G. Rewoldt.

PROGRAM SUMMARY
Title of program: GeneralVectorAnalysis
Catalogue identifier: ADJP
Ref. in CPC: 116(1999)107
Operating system: Win95, Unix, Linux
High speed store required: 20MK words
Number of lines in distributed program, including test data, etc: 1171
Programming language used: Mathematica
Computer: Pentium II 150 MHz PC

Nature of physical problem:
The analytical calculations using vector calculus that appear in plasma physics, fluid dynamics, and other fields sometimes can become extremely complex. The complexity usually originates from both the vector operations themselves and the underlying coordinate systems.

Method of solution
To implement automatic symbolic vector analysis in general coordinate systems, we need a simple and systematic mathematical framework. The modern viewpoint of 3D vector calculus, differential forms on 3-manifolds, is utilized for this purpose. On the other hand, a well- developed high level programming language with a symbolic computation capability is also necessary. To the end, we chose Mathematica by Wolfram Research Inc.

Typical running time
Running time is problem and machine dependent. Running Mathematica 3.0 on a Pentium II 150 MHz PC with 48M memory, is takes about 2 second CPU time to carry out a single vector differential operation to the second order of the inverse aspect ratio in the large aspect ratio circular concentric tokamak coordinate system.

Unusual features of the program
Asymptotic capabilities, 2D vector analysis notation, and a simple interface for users to define their own coordinate systems.